A dead end is similar to an assigned flow, except the flow rate is zero (Wylie, et al, 1993Wylie, E.B., V.L. Streeter & L. Suo, Fluid Transients in Systems, Prentice Hall, Englewood Hills, New Jersey, 1993., pp. 44). The unknown is then the pressure, which can be solved by calling the appropriate compatibility equation.If the dead end is at the upstream end of the pipe, the negative compatibility equation is used with zero flow.

Conversely, if the dead end is at the downstream end, the positive compatibility equation is used with zero flow.

Dead End Vapor Cavitation Theory

When the calculated pressure at a Dead End junction drops below vapor pressure, a vapor cavity forms at the junction.

Assuming the dead end is at the end of a pipe, the vapor volume calculation is as follows:

since the ṁ_downterms are always zero. For dead ends at the beginning of a pipe, the ṁ_up terms are zero. Similar to a pipe interior node, when the vapor volume is negative, the cavity collapses and the fluid pressure then rises above the vapor pressure.